Is it obligatory for someone who masturbated during the daytime in Ramadan, believing it did not break the fast, then later realized that it did, to make up those days, despite not knowing their exact number?

The madhhab of Shaykh Al-Albani and Ibn Hazm is that masturbation during the day in Ramadan does not invalidate the fast. Therefore, whoever follows them in this does not have to make up the fast.

However, it is preferable to follow the madhhab of the majority, who hold that making up the fast is obligatory, in order to avoid disagreement. So, you should make up the days on which you masturbated, and continue to make them up until you are reasonably certain that you have fulfilled your obligation.